Meeting Details

If $G$ and $H$ are finitely generated groups, $H$ is given by a presentation $< X | r=1, r\in R>$, then homomorphisms $H\to G$ corresponds to solutions of the system of equations $r=1, r\in R$ in $G$. If $H$ has infinitely many homomorphisms into $G$ (up to conjugacy in $G$), then $H$ acts non-trivially on the asymptotic cone of $G$. Together with J. Behrstock and C. Drutu, we apply this idea to homomorphisms into the Mapping Class Group of a surface. We prove, in particular, that if $H$ has Kazhdan property (T), then it has only finitely many homomorphisms into a mapping class group (up to
conjugacy).